...

Chhi Phuong

10/08/2017 at 21:54
Answers
1
Follow

Cho các đa thức :

F(x)=−x4−3x3+x2−2x+5−x4−3x3+x2−2x+5

G(x)=64+x3−2x2−3x−364+x3−2x2−3x−3

H(x)=−5x4+2x3+2x2+9x+3−5x4+2x3+2x2+9x+3

a)Tính F(x)+G(x)+H(x) và 2.F(x) - [G(x)+H(x)]

b)Tính giá trị F(-1),G(\(\dfrac{-1}{2}\));H(2)

c)Chứng minh rằng F(x)+G(x)+H(x) >0

d)Tìm x để giá trị của F(x)+G(x)+H(x) bằng 1



    List of answers
  • ...
    Phan Thanh Tinh Coordinator 11/08/2017 at 00:23

    a) \(F\left(x\right)+G\left(x\right)+H\left(x\right)=x^2+4x+5\)

    \(2F\left(x\right)-\left[G\left(x\right)+H\left(x\right)\right]\)

    \(=-2x^4-6x^3+2x^2-4x+10-\left(x^4+3x^3+6x\right)\)

    \(=-3x^4-9x^3+2x^2-10x+10\)

    b) \(F\left(-1\right)=-1+3+1+2+5=10\)

    \(G\left(-\dfrac{1}{2}\right)=\dfrac{3}{8}-\dfrac{1}{8}-\dfrac{1}{2}+\dfrac{3}{2}-3=-\dfrac{7}{4}\)

    \(H\left(2\right)=-80+16+8+18+3=-35\)

    c) \(F\left(x\right)+G\left(x\right)+H\left(x\right)=x^2+4x+5=x^2+4x+4+1\)

    \(=\left(x+2\right)^2+1>0\)

    d) \(x^2+4x+5=1\Leftrightarrow\left(x+2\right)^2+1=1\Leftrightarrow x=-2\)



Weekly ranking